Cornett, who had 70 yards rushing, scored on the ground from 7 and 3 yards and 1 yard. In the fourth quarter, he caught a 12-yard TD pass for the Rebels (2-8, 2-4 Mountain West), who ended a five-game losing streak.
Clayton was 13 of 18 passing 163 yards with no interceptions. He also rushed for 50 yards on 11 carries and caught a pass for 16 yards.
Alvester Alexander led Wyoming (2-8, 0-7) with 92 yards rushing, including a 72-yard run on the game's first play from scrimmage. Austyn Carta-Samuels was 13 of 22 for 108 yards with an interception for the Cowboys, who have lost six straight.